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Experimental phase control of a forced Chua's circuit

Mattia Frasca, Luigi Fortuna, Stefano Euzzor, Riccardo Meucci, F. T. Arecchi, Giovanni Chessari
The techniques to control chaos can be classified in feedback and open loop methods \cite{boccaletti00}. Feedback methods usually allow the system to be stabilized in any of the unstable periodic orbits lying in the chaotic attractor, but require fast and accurate response to work properly. On the other hand, open loop techniques usually exploit the effect of some (small) perturbations added to the system to modify the final state of the controlled dynamics.

An open loop technique used for periodically driven chaotic system is the so-called phase control \cite{Qu95,Yang96}. According to this control scheme, a further periodic forcing term is added to the system at the same frequency of the main driving signal, but with a different phase. It has been shown that the phase difference between these two forcing terms may act as a control parameter for the system \cite{Qu95,Yang96,Zambrano06}. In particular, in many systems a correct choice of the phase allows to suppress chaos with a very small amplitude harmonic perturbation. Phase control has been applied to the Duffing system \cite{Qu95,Yang96,Zambrano06}, to control intermittency in a
$CO_2$ laser \cite{Zambrano06PRE} and to avoid escapes of a Helmholtz oscillator \cite{Seoane08}.

Both non-feedback and feedback techniques have been applied to the Chua's circuit \cite{frascabook}. In this paper we investigate the suitability of the phase control technique to suppress chaos in a driven Chua's circuit.
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